Transcript of Gaussian KD-Tree for Fast High-Dimensional Filtering A. Adams, N. Gelfand, J. Dolson, and M. Levoy,...
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- Gaussian KD-Tree for Fast High-Dimensional Filtering A. Adams,
N. Gelfand, J. Dolson, and M. Levoy, Stanford University, SIGGRAPH
2009.
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- Edge-Preserving Filtering Noise Suppression Detail Enhancement
High Dynamic Range Imaging
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- Edge-Preserving Filtering for Image Analysis Input Image Base
ImageDetail Image
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- Edge-Preserving Vs. Edge-Blurring Input Image Edge-Preserving
Base ImageEdge-Blurring Base Image
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- Edge-Preserving Vs. Edge-Blurring Edge-Preserving Enhanced
ImageEdge-Blurring Enhanced Image Halo Artifacts
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- Gaussian Filtering
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- Bilateral Filtering Output Input Space WeightRange Weight Space
WeightRange Weight x y Intensity
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- Bilateral Filtering Output Input Bilateral Weight Space
WeightRange Weight x y Intensity
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- Bilateral Filtering Input ImageGaussian: p = 12 Bilateral: p =
12, c = 0.15
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- Computational Complexity of Bilateral Filtering O(n 2 d) Image
Size: n Maximum Filter Size: n Dimension: d High Computational
Complexity Input x y Intensity
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- Novel Methods Bilateral Grid J. Chen, S. Paris, and F. Durand,
Real-time edgeaware image processing with the bilateral grid, ACM
Transactions on Graphics (Proc. SIGGRAPH 07). Gaussian KD-Tree A.
Adams, N. Gelfand, J. Dolson, and M. Levoy, Gaussian KD-Trees for
Fast High-Dimensional Filtering, ACM Transactions on Graphics
(Proc. SIGGRAPH 09).
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- High-Dimensional Filtering x y Intensity
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- A Two-Dimensional Example x I Space Range Signal Kernel x I
Output Signal Kernel Gaussian Filtering x I Space SignalOutput
Signal Bilateral Filtering Large Kernel Size High Computational
Complexity!
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- Bilateral Grid Downsampling x I Signal Bilateral Grid x I
Signal Spatial Grid Traditional Spatial Downsampling x I Signal
Bilateral Grid Bilateral Grid Downsampling x I Bilateral Grid
Kernel
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- Bilateral Filter on the Bilateral Grid Image scanline space
intensity Bilateral Grid
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- space intensity Bilateral Filter on the Bilateral Grid Image
scanline Filtered scanline Slice: query grid with input image
Bilateral Grid Gaussian blur grid values space intensity
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- Bilateral Filtering for Color Image Bilateral Filtering Based
on LuminanceBilateral Filtering Based on Color
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- Bilateral Grid for Color Image Image High-Dimensional Grid (5d
grid) High Memory Usage Cost
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- Gaussian KD-Tree Low Computational Complexity Low Memory
Usage
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- Gaussian KD-Tree Building The Tree Querying The Tree
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- Building The Tree Space Intensity Bounding Box Longest
Dimension, 1 d 1 min 1 max 1 cut 11 Gaussian KD-Tree
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- Building The Tree Space Intensity 2d2d 2 min 2 max 2 cut 11
Gaussian KD-Tree 22 22
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- Building The Tree Space Intensity 3d3d 3 min 3 max 3 cut 11
Gaussian KD-Tree 22 33 33
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- Building The Tree Space Intensity 4d4d 4 min 4 max 4 cut 11
Gaussian KD-Tree 22 44 33 44
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- Building The Tree Space Intensity Inner Node Cutting Dimension
Min, Max Bound Left, Right Child 11 Gaussian KD-Tree 22 33 44
.
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- Building The Tree Space Intensity Leaf Node Position
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- Querying The Tree 11 Gaussian KD-Tree 22 33 44 .
High-Dimensional Space Image Pixel Querying
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- Querying The Tree Gaussian KD Tree Inner Node Leaf Node Image
Pixel Different Weighting to Leaf Nodes
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- Splatting
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- 1-D Example of Splatting Space Querying Position Space Querying
Position cut Sample Distribution cut Splatting
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- 1-D Example of Splatting Space Querying Position Space Querying
Position cut Sample Distribution cut Splatting
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- Correcting Weights for Splatting q pi
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- Querying The Tree Gaussian KD Tree Inner Node Leaf Node Image
Pixel Sample Splitting to Leaf Nodes Samples
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- Blurring The Leaf Nodes
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- Slicing
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- Summary x y r,g,b Input Image Gaussian KD Tree High-Dimensional
Space Resolution Reduction Monte-Carlo Sampling Weighted Importance
Sampling
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- Applications Bilateral Filtering Nave Bilateral Filtering 5-D
Bilateral Grid
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- 3-D Bilateral Grid KD-Tree
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- Complexity and Performance Analysis Filter Size Large Small 5D
Grid Gaussian KD-Tree Nave
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- Applications Non-local Mean Filtering Input ImageOutput
Image
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- Non-local Mean Filtering Target Patch Searching Patches ..
Patch
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- Non-local Mean Filtering with PCA Patch Examples 16 Leading
Eigenvectors
http://www.ceremade.dauphine.fr/~peyre/numerical-tour/tours/denoising_nl_means/
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- Non-local Mean Filtering Target Patch Searching Patches ..
Patch High-Dimensional Space
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- Non-local Mean Filtering with Gaussian KD-Tree Gaussian KD Tree
Inner Node Leaf Node Image Pixel Different Weighting to Leaf Nodes
High-Dimensional Space
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- Applications Non-local Mean Filtering Input ImageOutput
Image
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- Applications Geometry Filtering Input ModelOutput Model with
Gaussian Filtering Output Model with Non-local Mean
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- Conclusions Novel methods of non-linear filter. Bilateral grid
and Gaussian kd-tree High-dimensional non-linear filter. Edge
preserving smoothing Computational Complexity Reduction Importance
sampling